Put-Call Parity
Put-call parity is the no-arbitrage link C − P = F − K (discounted) — a European call and put with the same K and T are one instrument plus cash.
Definition
For European options on a non-dividend asset: C − P = S − K e^{−rT} (adjust for dividends/borrow). Violations are conversions and reversals. American options break strict parity because of early exercise.
Why it matters
It is how you synthesize a forward and how you spot a mispriced wing. Implied forward from C−P is a desk check on the listed chain.
Case
Hard-to-borrow stock: put-call implied forward sits below cash because the call is heavy and the put is bid. Parity is holding; the borrow is the story.
How to read it
Use Europeans or correct for early exercise. If parity ‘fails,’ look at borrow, dividends, and American premium before you click arb.
Key papers
Landmark references with real publisher or arXiv links — not token-overlap noise.
- The Pricing of Options and Corporate LiabilitiesBlack, Scholes · 1973 · Journal of Political EconomyParity sits underneath the European formula.